Osborne and Waters (2002) focused on checking some of the assumptions of multiple linear regression. In a critique of that paper, Williams, Grajales, and Kurkiewicz correctly clarify that regression models estimated using ordinary least squares require the assumption of normally distributed errors, but not the assumption of normally distributed response or predictor variables.They go on to discuss estimate bias and provide a helpful summary of the assumptions of multiple regression when using ordinary least squares. While we were not as precise as we could have been when discussing assumptions of normality, the critical issue of the 2002 paper remains -researchers often do not check on or report on the assumptions of their statistical methods. This response expands on the points made by Williams, advocates a thorough examination of data prior to reporting results, and provides an example of how incremental improvements in meeting the assumption of normality of residuals incrementally improves the accuracy of confidence intervals. Accessed 6,654 times on https://pareonline.net from September 06, 2013 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right.
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Osborne, Jason W.
"Normality of residuals is a continuous variable, and does seem to influence the trustworthiness of confidence intervals : A response to, and appreciation of, Williams, Grajales, and Kurkiewicz (2013),"
Practical Assessment, Research, and Evaluation: Vol. 18
, Article 12.
Available at: https://scholarworks.umass.edu/pare/vol18/iss1/12